Heel and toe downshifting is a technique that allows you to raise the revs of your engine to match the wheel speed when you shift into a lower gear.   It reduces strain on the transmission, and on a racetrack it permits downshifts in the middle of high-speed turns that will not upset the car's balance or wheel grip.   It's seldom necessary on the street, but the street is a good place to learn this skill.

Here is a step-by-step guide on how to do it.   In this example, the shift will be from fourth gear down to third.

1. Begin braking for the corner with your right foot.   The location of the pedals and the size of your foot will dictate where you position your foot on the pedal, but most likely it should be canted a little to the right, closer to the throttle pedal.

2. Push in the clutch with your left foot.

3. Move the shifter from fourth gear to neutral.

4. With your right foot still applying pressure to the brakes, roll the outside edge of your foot outward and downward to touch the throttle pedal.   The pedal design on some cars makes this easier to do than on others.

5. Use the outside of your right foot to blip the throttle.   Blipping the throttle means temporarily raising the engine rpms to match the wheel speed.   The exact amount of revs needed is dependent on a variety of factors, but it is usually between 1,000 rpm to 2,000 rpm more than the current engine rpm for a one-gear downshift.

6. Move the shifter from neutral to third gear.

7. Release the clutch with your left foot.

When you do the heel and toe right, shifting to the lower gear is easy on your transmission because the lower gears have been spun up to match your wheel speed.

The tricky part is getting the correct amount of rpms to match the new gear.   If you blip the throttle too much, the engine has too much speed compared to the wheels and is forced to drop down to the wheel speed when you let out the clutch.   If you don't blip the throttle enough, the engine rpms are forced to rise up. Either way, you know you didn't do it right as the car will jerk a little.  

You need to practice a lot.   I'm told that eventually it will become second nature.   It hasn't yet for me... But I'm working on it.